Renormalization and unitarity in higher derivative and nonlocal gravity theories

2015 ◽  
Vol 30 (03n04) ◽  
pp. 1540005 ◽  
Author(s):  
E. T. Tomboulis
Keyword(s):  
Quantum Gravity ◽  
Fixed Points ◽  
Fourth Order ◽  
Entire Functions ◽  
Gravitational Action ◽  
Asymptotic Safety ◽  
Higher Derivative ◽  
Fixed Order ◽  
Gravity Theories

We review and discuss higher derivative and nonlocal theories of quantum gravity focusing on their UV and unitarity properties. We first consider the general fourth-order gravitational action, then actions containing derivatives up to any given fixed order, and discuss their UV divergences, fixed points and concomitant unitarity issues. This leads to a more general discussion of "asymptotic safety" and unitarity, which motivates the introduction of nonlocal theories containing derivatives to all orders arising from the expansion of entire functions. For such theories good UV behavior is visible at any finite truncation, but unitarity emerges only when derivatives to all orders are included.

scholarly journals ASYMPTOTIC SAFETY IN HIGHER-DERIVATIVE GRAVITY

2009 ◽  
Vol 24 (28) ◽  
pp. 2233-2241 ◽  
Author(s):  
DARIO BENEDETTI ◽  
PEDRO F. MACHADO ◽  
FRANK SAUERESSIG
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Renormalization Group Flow ◽  
Functional Renormalization Group ◽  
Asymptotic Safety ◽  
Higher Derivative ◽  
Gravity Theories ◽  
Group Flow ◽  
Nonperturbative Renormalization

We study the nonperturbative renormalization group flow of higher-derivative gravity employing functional renormalization group techniques. The nonperturbative contributions to the β-functions shift the known perturbative ultraviolet fixed point into a nontrivial fixed point with three UV-attractive and one UV-repulsive eigendirections, consistent with the asymptotic safety conjecture of gravity. The implication of this transition on the unitarity problem, typically haunting higher-derivative gravity theories, is discussed.

scholarly journals Black holes within asymptotic safety

2014 ◽  
Vol 29 (08) ◽  
pp. 1430011 ◽  
Author(s):  
Benjamin Koch ◽  
Frank Saueressig
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Quantum Gravity ◽  
Space Time ◽  
Asymptotic Safety ◽  
Angular Momenta ◽  
Higher Derivative ◽  
The Status ◽  
Time Singularities ◽  
Characteristic Features

Black holes are probably among the most fascinating objects populating our universe. Their characteristic features found within general relativity, encompassing space–time singularities, event horizons, and black hole thermodynamics, provide a rich testing ground for quantum gravity ideas. We review the status of black holes within a particular proposal for quantum gravity, Weinberg's asymptotic safety program. Starting from a brief survey of the effective average action and scale setting procedures, an improved quantum picture of the black hole is developed. The Schwarzschild black hole and its generalizations including angular momenta, higher-derivative corrections and the implications of extra dimensions are discussed in detail. In addition, the quantum singularity emerging for the inclusion of a cosmological constant is elucidated and linked to the phenomenon of a dynamical dimensional reduction of space–time.

scholarly journals On the Structure of the Vacuum in Quantum Gravity: A View from the Asymptotic Safety Scenario

Universe ◽  
2019 ◽  
Vol 5 (8) ◽  
pp. 182 ◽  
Author(s):  
Alfio Bonanno
Keyword(s):  
Quantum Gravity ◽  
Degrees Of Freedom ◽  
Vacuum State ◽  
Critical Surface ◽  
Asymptotic Safety ◽  
Quantum Chromo Dynamics ◽  
Full Theory ◽  
Higher Derivative ◽  
Quadratic Gravity ◽  
Non Gaussian

Although the Asymptotic Safety scenario is one of the most promising approaches to quantum gravity, little attention has been devoted to the issue of the vacuum state. Higher derivative operators often appear on the ultraviolet critical surface around the non-Gaussian fixed point generating additional degrees of freedom which can render the standard vacuum unstable. When this happens, translation and rotational symmetries can be spontaneously broken and a new set of symmetries can show up at the level of the effective action. In this work, it will be argued that a “kinetic condensate” characterizes the vacuum state of asymptotically safe quadratic gravity theories. If this scenario is realized in the full theory, the vacuum state of gravity is the gravitational analogous to the Savvidy vacuum in Quantum Chromo-Dynamics (QCD).

scholarly journals Noisy effects in interferometric quantum gravity tests

2017 ◽  
Vol 15 (08) ◽  
pp. 1740014 ◽  
Author(s):  
F. Benatti ◽  
R. Floreanini ◽  
S. Olivares ◽  
E. Sindici
Keyword(s):  
Quantum Gravity ◽  
Weak Coupling ◽  
Scale Effects ◽  
External Environment ◽  
Planck Scale ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
Photon Propagation ◽  
Gravity Theories ◽  
Planck Scale Effects

Quantum-enhanced metrology is boosting interferometer sensitivities to extraordinary levels, up to the point where table-top experiments have been proposed to measure Planck-scale effects predicted by quantum gravity theories. In setups involving multiple photon interferometers, as those for measuring the so-called holographic fluctuations, entanglement provides substantial improvements in sensitivity. Entanglement is however a fragile resource and may be endangered by decoherence phenomena. We analyze how noisy effects arising either from the weak coupling to an external environment or from the modification of the canonical commutation relations in photon propagation may affect this entanglement-enhanced gain in sensitivity.

Gauge invariance and unitarity in higher-derivative quantum gravity

1986 ◽  
Vol 33 (10) ◽  
pp. 2756-2779 ◽  
Author(s):  
I. Antoniadis ◽  
E. T. Tomboulis
Keyword(s):  
Quantum Gravity ◽  
Gauge Invariance ◽  
Higher Derivative

scholarly journals Chaos and Stability in a New Iterative Family for Solving Nonlinear Equations

Algorithms ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 101
Author(s):  
Alicia Cordero ◽  
Marlon Moscoso-Martínez ◽  
Juan R. Torregrosa
Keyword(s):  
Fixed Points ◽  
Periodic Orbits ◽  
Nonlinear Equations ◽  
Fourth Order ◽  
Complex Dynamics ◽  
Convergence Properties ◽  
Parameter Spaces ◽  
Numerical Tests ◽  
The Family ◽  
Dynamics Stability

In this paper, we present a new parametric family of three-step iterative for solving nonlinear equations. First, we design a fourth-order triparametric family that, by holding only one of its parameters, we get to accelerate its convergence and finally obtain a sixth-order uniparametric family. With this last family, we study its convergence, its complex dynamics (stability), and its numerical behavior. The parameter spaces and dynamical planes are presented showing the complexity of the family. From the parameter spaces, we have been able to determine different members of the family that have bad convergence properties, as attracting periodic orbits and attracting strange fixed points appear in their dynamical planes. Moreover, this same study has allowed us to detect family members with especially stable behavior and suitable for solving practical problems. Several numerical tests are performed to illustrate the efficiency and stability of the presented family.

scholarly journals Standard model and graviweak unification with (super)renormalizable gravity. Part I: Visible and invisible sectors of the universe

2015 ◽  
Vol 30 (09) ◽  
pp. 1550044 ◽  
Author(s):  
L. V. Laperashvili ◽  
H. B. Nielsen ◽  
A. Tureanu
Keyword(s):  
Standard Model ◽  
Quantum Gravity ◽  
Consistent Theory ◽  
Invariant Model ◽  
Higher Derivative ◽  
Self Consistent ◽  
Renormalizable Theory ◽  
Theory Of Gravity ◽  
Higgs Fields ◽  
The Universe

We develop a self-consistent Spin (4, 4)-invariant model of the unification of gravity with weak SU(2) gauge and Higgs fields in the visible and invisible sectors of our universe. We consider a general case of the graviweak unification, including the higher-derivative super-renormalizable theory of gravity, which is a unitary, asymptotically-free and perturbatively consistent theory of the quantum gravity.

scholarly journals Holographic entanglement entropy, field redefinition invariance, and higher derivative gravity theories

2016 ◽  
Vol 94 (4) ◽  
Author(s):  
M. R. Mohammadi Mozaffar ◽  
A. Mollabashi ◽  
M. M. Sheikh-Jabbari ◽  
M. H. Vahidinia
Keyword(s):  
Entanglement Entropy ◽  
Holographic Entanglement Entropy ◽  
Higher Derivative ◽  
Gravity Theories ◽  
Field Redefinition

scholarly journals The Asymptotic Safety Program for Quantum Gravity

2012 ◽  
Author(s):  
Frank Saueressig ◽  
Kai Groh ◽  
Stefan Rechenberger ◽  
Omar Zanusso
Keyword(s):  
Quantum Gravity ◽  
Safety Program ◽  
Asymptotic Safety
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